Due to its widespread application in the robotics field, the Kalman filter has received increased attention from researchers. This work reviews some of the modifications conducted on to this algorithm over the last years. Problems such as the consistency, convergence, and accuracy of the filter are also dealt with. Sixty years after its creation, the Kalman filter is still used in autonomous navigation processes, robot control, and trajectory tracking, among other activities. The filter is not only restricted to robotics but is also present in different fields, such as economics and medicine. In addition, the characteristics of each modification on this filter are analyzed and compared.

The study of lower limbs has become relevant in recent years. Lower limbs have several classifications, but the most widespread categories are robots for patient rehabilitation and robots for work tasks. Two of the main pillars in the development of exoskeletons are actuators and control strategies. Pneumatic artificial muscles are similar to human muscles in their function. This work focuses on this similarity to develop control techniques for this type of actuator. The purpose of this investigation is to design, evaluate, and compare the effectiveness of three different control systems—the proportional–integrative–derivative (PID) system, the sliding mode control (SMC) system, and the fuzzy logic controller (FLC) system—in executing precise trajectory tracking using an exoskeleton and including very realistic dynamic considerations. This study aims to design and implement these controllers and assess their performance in following three distinct trajectories, thereby determining the most efficient and reliable control method for exoskeleton motion. Additionally, the analysis centers on both the response of the controllers to external perturbations and the reaction of the controllers when the time delay inherent to their dynamic is added to the mathematical model. Finally, the results are compared, revealing through the analysis of performance indexes and time response that the FLC is the controller that exhibits the best global results in the tracking of the different trajectories. This work demonstrates that, for the system in question, the action of adding a time delay in the actuator causes the FLC and PID controllers to maintain a similar response, which is obtained without the delay action, in contrast to the system with an SMC controller. However, the same does not occur when including other dynamic factors, such as disturbances external to the system.

Given the widespread use of the Kalman filter in robotics, an increasing number of researchers devote themselves to its study and application. This work underscores the importance of this filter while analyzing the modifications made to the same to improve its performance and reduce its deficiencies in some fields and presenting some of its applications in robotics. The following methods are presented in this study: least squares (LS), Hopfield Neural Networks (HNN), Extended Kalman filter (EKF), and Unscented Kalman filter (UKF). These methods are used in the parameter identification of a Selective Compliant Assembly Robot Arm (SCARA) robot with 3-Degrees of Freedom (3-DoF) and a clamp at its end. The dynamic model of this robot is obtained and employed to identify its parameters; then, the identification results are compared considering the difference between the obtained parameters and the real values of the robot parameters; in this comparison, the good results yielded by the LS and UKF method stand out. Subsequently, the obtained parameters through each method are validated by measuring different performance indexes—during trajectory tracking—such as: Residual Mean Square Error (RMSE), Integral of the Absolute Error (IAE), and the Integral of the Square Error (ISE). In this way, a comparison of the robot’s performance is possible.

This work presents the design and assessment of four control schemes for the monitoring and regulation of joint trajectories applied in the dynamic model of a SCORBOT-ER V plus robot, which includes the dynamics of the actuators, and the estimation of the friction forces present within the joints. The two classical control strategies calculated torque and PID, and the two advanced control strategies, fuzzy and predictive, are considered. In the latter case, a gravitational compensation stage is incorporated, as well as the inverse models of the motors and the transmissions of belt movement for each joint. Computational tests are performed by applying an external step-type disturbance to the third joint of the robot. Finally, an evaluation of the results obtained is presented through trajectory curves, joint errors, and the three performance indexes residual mean square, residual standard deviation, and index of agreement.